We will talk about the Fourier restriction theorems for non-degenerate and degenerate curves in Euclidean space R^{d}. This problem was first studied by E. M. Stein and C. Fefferman for the circle and sphere, and it still remains an unsolved problem for the sphere in dimension larger than 2. Our problem is an analogous problem for curves. We will also mention an extension of such results to some complex curves in R^{2d}. These are 2-dimensional surfaces defined by certain complex functions.